Optical interconnection device

ABSTRACT

An optical interconnection device suitable for an N×N&#39; coupler as used, for example, in a local area network, comprises diffraction means in the form of a body having a refractive index which varies spatially and periodically in one plane of the body. The arrangement is such that light incident upon the body in the plane and at a predetermined angle will be refracted to emerge at a plurality of discrete angles determined by the spatially varying refractive index. The incident light is distributed substantially equally among the plurality of output refracted beams and substantially all of said incident light is coupled to the plurality of refracted beams. The diffraction means comprises a cylindrical body, and the device further comprises two arrays of optical sources and/or receivers. The arrays are disposed at opposite faces, respectively, of the body, each of the optical receivers having an optical axis aligned with one of the discrete angles. A perfect shuffle network may comprise a plurality of nodes interconnected by such a coupler, each node comprising a transmitter operable at several wavelengths a receiver, and means for determining whether a received signal is to be relayed and, if so, the appropriate transmission wavelength.

This is a continuation-in-part of International patent applicationnumber PCT/CA 90/00119, filed Apr. 11, 1990 and designating the UnitedStates of America.

FIELD OF THE INVENTION

This invention relates to optical devices, and is especially, but notexclusively, applicable to N×N' interconnectors or couplers such as areused in local area networks and backplanes of telecommunications andcomputer equipment. Embodiments of the invention may also be used tointerconnect components in integrated circuits, to interconnectintegrated circuits on a circuit board, and in analogous situations inthe field of optical communications, especially where single modeoptical fibres are to be interconnected.

The invention also relates to optical interconnects or couplers havinglimited or selective coupling capability in that each input port iscoupled to preselected ones of a plurality of output ports. Theinvention also encompasses lightwave communications systemsincorporating such couplers and, for example, the so-called "multihop"networks including the afore-mentioned couplers having limited orselective coupling capability.

In this specification, the term "optical" is used to embrace bothvisible and invisible lightwaves.

BACKGROUND

An N×N' star coupler is one of the key elements in Local Area Network(LAN) applications of optical fibre. The simplest single-mode 2×2 starcoupler can be manufactured by bringing the cores of two single-modefibres sufficiently close together over an appropriate coupling length.Various such structures have been built by using etching, grinding andpolishing, or fusion. A 2×2 star coupler can be used as a basic buildingblock to construct larger N×N' couplers where N is equal to an arbitrarypower of two. However, this involves interconnecting a large number of2×2 couplers, increasing the excess loss for larger values of N.

European patent application number 0340987, published Nov. 8, 1989,[which is incorporated herein by reference] discloses an N×N' staroptical coupler comprising a dielectric slab and two arrays of stripwaveguide formed on a glass substrate. Opposite surfaces of thedielectric slab, to which the strip waveguides are attached, are curved.The radius of curvature and the distance between the surfaces are suchthat the optical axis of each waveguide at one surface extends radiallyacross the slab to the centre of the other curved surface.

The configuration is said to provide even distribution of light fromeach waveguide to the waveguide at the opposite side of the dielectricslab. The optimized efficiency of such a coupler varies between 0.34 atthe edge and 0.55 at the middle of the array, which is not entirelysatisfactory. This gives better coupling efficiency compared with a slabhaving parallel sides, in which light from a particular input waveguidewill cover more than the entire area of the opposite face, so it isrelatively inefficient since much of the light is diffused before itreaches the output side of the coupler.

U.S. Pat. No. 4,057,319 discloses a coupler connecting one fibre in abundle to the fibre in another bundle. A phase hologram plate isinterposed between an input bundle of fibres and the output bundle offibres. The phase hologram effectively focuses the light onto the outputoptical fibre and so improves coupling efficiency. A disadvantage ofthis device is that it is suitable only for individual connections andhence not suitable for applications requiring N×N' coupling.

U.S. Pat. No. 4,838,630, issued Jun. 13, 1989 [and incorporated hereinby reference] discloses a planar optical interconnector for 1×N or N×1coupling in interconnecting integrated circuits. The interconnectorcomprises a Bragg planar volume hologram which distributes opticalsignals, but is not capable of N×N' coupling.

U.S. Pat. No. 4,705,344, issued Nov. 10, 1987, [which is incorporatedherein by reference] disclosed an interconnection device for opticallyinterconnecting a plurality of optical devices. The interconnectiondevice comprises an optically transparent spacer with photosensitivematerial on its opposite sides. Fringes are formed, fixedly positioned,on one of the surfaces. The fringes comprise a plurality of"sub-holograms". The other surface has positions for the opticaldevices. The fringe pattern is formed by directing a coherent light beamthrough the spacer and photosensitive material to one position anddirecting a second coherent light beam from a second position tointerfere with the first beam. Each source device emits a light beamwhich traverses the transparent spacer, is reflected by the holograph onthe opposite face, and returns to a different position. The hologram is,in effect a plurality of discrete holograms each one dedicated to onepair of positions. This kind of interconnection device provides logicfunctions for optical computing but is limited to 1×N coupling.

Thus, none of these known devices can provide N by N coupling with anefficiency and simplicity which can be considered satisfactory.

There remains a need for an optical interconnector with improvedcoupling efficiency for use in coupling single mode waveguides, forexample optical fibres, in a number of applications such as local areanetworks, back planes of telephone switches and also in integratedcircuits or circuit boards and similar situation where a large number ofconnections need to be made in a very limited space.

SUMMARY OF INVENTION

According to one aspect of the invention, there is provided an opticaldevice comprising a stratified volume Bragg diffraction means, forexample a hologram, having its refractive index varying spatiallyaccording to the expression: ##EQU1## where

x and z are ordinates of the block;

k_(m),m' * is the spatial frequency vector;

m is an input position or mode, corresponding to one optical axis;

m' is an output position or mode, corresponding to one optical axis;

m and m' taking on integer values that determine the number ofinput/output modes;

Δ_(m),m' is the coefficient of coupling between m and m'; and

r is the space vector.

In one, preferred, embodiment of the present invention, suitable forinterconnecting optical communication channels, the device comprises abody having cylindrical opposed faces, said stratified volume Braggdiffraction means being provided in said body such that its refractiveindex varies spatially and periodically in one plane of the body, thearrangement being such that a planar light wave incident upon one ofsaid faces of the body in said plane, at a predetermined angle, with theelectric field of such light wave extending in the same direction as theaxes of said cylindrical opposed faces, will be refracted to emerge atone or more discrete angles determined by the spatially varyingrefractive index, such incident light being distributed substantiallyequally among the plurality of output refracted beams.

Such a diffraction means may be arranged to couple substantially all ofthe input light to the predetermined refracted beams, i.e. with minimalloss.

According to another aspect of the invention, an N×N' opticalinterconnector comprises a planar body having cylindrical opposed facesand two arrays of optical sources and/or receivers, said arrays beingdisposed one at each of said faces, respectively, said body having arefractive index which varies spatially and periodically with theelectric field of such light wave extending in the same direction as theaxes of said cylindrical opposed faces, such that light emanating fromeach of said sources is distributed equally among the receivers at theopposite face.

In such embodiments, the refractive index n(x,z) of the stratifiedvolume Bragg diffraction means varies spatially in accordance with theexpression: ##EQU2## where

x and z are ordinates of the block;

d is the radius of curvature of the curved faces;

k_(m),m' * is the spatial frequency vector;

m is an input position or mode, corresponding to one optical axis;

m' is an output position or mode, corresponding to one optical axis;

m and m' taking on integer values that determine the number ofinput/output modes;

Δ_(m),m' is the coefficient of coupling between m and m';

r is the space vector; and

N is the total number of modes and is equal to 2M+1.

The optical sources/receivers may comprise waveguides, for exampleoptical fibres, or electro-optic devices for directing or receivinglight. Each optical source is positioned so as to direct light along anoptical axis extending radially of one face to the middle of theopposite face. Conversely, each optical receiver is positioned toreceive light along an optical axis extending radially of the face withwhich the receiver is associated from the middle of the opposite face.Preferably the arrangement is such that substantially all of the lightfrom each source is received by the optical receivers.

According to still another aspect of the invention, there is provided amethod of making a diffraction means for an optical interconnector byirradiating a body of photorefractive material having cylindricalopposed faces using a two wave mixing process employing two light beamscomprising substantially planar waves, the method comprising the stepsof:

(i) aligning the body with its cylindrical axes transverse to the planeof said substantially plane waves;

(ii) directing one of said light beams across said body in said plane;

(iii) directing the other of said light beams across said body, in saidplane, in succession, at a plurality of predetermined angles to thefirst light beam;

(iv) directing said one of said light beams across said body at adifferent angle and repeating steps (iii) and (iv), such that therefractive index of the irradiated body varies spatially andperiodically in the plane of said waves, such that light incident uponsaid body in said plane at one of said discrete angles will be refractedto emerge in said plane at a plurality of different angles.

According to a further aspect of the invention, a method of making adiffraction means for an optical interconnector comprises the steps of:

(i) irradiating a planar body of photorefractive material by means of afirst coherent light source along an axis at a predetermined axis to thebody, the light comprising a substantially planar wave in the plane ofthe body;

(ii) irradiating the body by means of a second coherent light sourcealong an axis at a predetermined axis to the light from the firstsource, and p (iii) recording the resulting interference pattern in theslab;

(iv) maintaining the position of the first source,

(v) rotating the second source stepwise, each step by a predeterminedangle, and repeating steps (i), (ii) and (iii), for each step; rotatingthe first source stepwise by a plurality of predetermined angles and,for each step, repeating step (v).

According to yet another aspect of the invention, apparatus forproducing a diffraction means for an optical interconnection devicecomprises first and second sources of substantially planar light wave,means for supporting a body of photorefractive material, said bodyhaving cylindrical opposed faces, so as to be irradiated by light fromboth said sources, the electric fields of the planar light wavesextending in the same direction as the cylindrical axes of said opposedfaces, means for rotating one of said sources stepwise relative to theother source and about an axis extending through said body, means forrotating the other source stepwise about the same point as the rotationof the first source, the resulting interference pattern being recordedin said body such that a light beam incident upon one of said opposedfaces will be refracted and distributed equally among a plurality ofoutput beams emerging from the other of said opposed faces.

According to a further embodiment of the invention, apparatus forproviding a diffraction means for an optical interconnector comprises:

a support for the body of photorefractive material having cylindricalopposed faces;

a plurality of optical devices in two planar arrays, one each side ofthe support, the devices being positioned with their optical axesextending radially from a common point and mutually spaced by apredetermined angle, said devices comprising plane wave light sourcesfor providing planar light waves with their electric fields extending inthe same direction as the cylindrical axes of said cylindrical opposedfaces;

means for selectively energizing pairs of said devices in succession tovary the refractive index of the body spatially and periodically in theplane of said arrays such that a light beam incident upon one of saidopposed faces will be refracted and distributed equally among aplurality of output beams emerging from the other of said opposed faces.

One embodiment of the present invention comprises an opticalinterconnection device which has its spatially-varying refractive indexconfigured so that each individual input light wave is coupled toselected ones of a plurality of outputs. Such a coupler findsapplication in so-called multihop lightwave communication networks.

The design of multigigabit local lightwave networks has received greatattention. Some of the proposed optical fiber based networks adoptpacket switching which was originally designed for data traffic. Thereis currently a trend to combine various types of traffic on one network.Various techniques have been proposed or developed for this purpose.These networks are intended for multi-user applications, e.g., local andmetropolitan area networks with potentially more than a terahertz ofbandwidth, even though each user is constrained by the electronics toaccess only a small portion of the available bandwidth. For example, ina wavelength division multiplexing (WDM) passive broadcast star network,although the rate at which any one user transmits information is limitedby the electronics, multiple users can transmit on wavelengths λ_(m)where m=1,2, . . . , N and the lightwaves are combined in the passivestar coupler. The superimposed light signals are made available to allthe receivers, with each receiver tuning to one wavelength. Adisadvantage of this approach is that pretransmission coordination isrequired so that each receiver knows to which channel it must tune foreach time interval. Also, users need to rapidly and accurately tune thereceivers (or transmitter) over the available band to allow any user tocommunicate with any other user.

In order to overcome these disadvantages of standard multichannelsystems, it has been proposed to use a so-called "multihop" approach. Ina multihop system, to transmit a packet from one user to another, mayrequire routing the packet through intermediate users, each repeatingthe packet on a new wavelength, until the packet is finally transmittedon a wavelength that the destination user receives. In other words, apacket may need to take multi hops to reach its destination. With themultihop approach, many packets are concurrently circulating through thenetwork; some fraction of these are new packets and the remainder arerepeated packets. U.S. Pat. No. 4,914,648 by A. Acampora et al., issuedApr. 3, 1990, discloses a multihop lightwave communication systemimplemented using a perfect shuffle topology.

Although such multihop networks offer advantages, a limitation can arisefrom the relaying of the signals. If a conventional passive star coupleris used, the data packets will be attenuated significantly each timethey traverse it.

An object of the present invention is to mitigate this problem.

According to yet another aspect of the invention, there is provided anoptical device comprising a stratified volume Bragg diffraction means,for example a hologram, having its refractive index varying spatiallyaccording to the expression: ##EQU3## wherein

sin(γ_(m) d)=1

m is an integer value where ##EQU4## and where

x and z are ordinates of the block;

k_(m),m' * is the spatial frequency vector;

m is an input position or mode, corresponding to one optical axis;

m' is an output position or mode, corresponding to one optical axis;

m and m' taking on integer values that determine the number ofinput/output modes;

Δ_(m),m' is the coefficient of coupling between m and m'; and

r is the space vector.

The physical configuration of such an optical interconnection device maybe similar to that described above with reference to the first aspect ofthe invention. It may also be made using much the same method ofmanufacture as described above.

A limited-broadcast coupler comprising such a body can be designed forvirtually any arbitrary shuffle network with the following parameters:

p: Degree of graph

I: Number of columns

N=Ip^(I) : Total number of interface nodes.

According to another aspect of the invention, there is provided acommunication network comprising a plurality of nodes interconnected bysuch a limited or selective coupler.

The limited-broadcast coupler effects the necessary physical connectionsof two successive columns of the shuffle network. Having access to sucha limited-broadcast coupler as a central piece of the network will makemany desired architectures feasible for future optical networks. Aspace-varying refractive index slab is introduced as a key designelement for such a coupler.

The network may comprise a plurality of said optical devices connectedin tandem, each device having a passband overlapping the passband of thedevice to which it is coupled, whereby signals having wavelengths withinthe overlapping regions of the band will be relayed through saidinterconnecting devices.

The network may be arranged such that the wavelengths of light beamstransmitted through the network are selected to correspond substantiallywith peaks of the period of the periodic refractive index.

In embodiments of each of the foregoing aspects of the invention, thespatial frequency vector k_(m),m' * is determined according to theexpression

    K.sub.m,m' *=|K.sub.m,m' *|(1.sub.x cosθm,m', 0, 1.sub.z sinθ.sub.m,m') ##EQU5## k is the optical wave vector (propagation factor ##EQU6## and where θ.sub.o is the angle between optical axes of adjacent inputs

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is plan view, partially cut away, of an optical interconnector;

FIG. 2 is a schematic representation of the optical interconnector.

FIG. 3(a), 3(b) and 3(c) depict refraction of an input light beam intothree specified modes;

FIG. 4(a), 4(b) and 4(c) illustrate coupling modes individually andcollectively;

FIG. 5 is a schematic diagram of apparatus for preparing a body having aspatially varying refractive index for use in the optical interconnectorof FIG. 1;

FIG. 6(a) and 6(b) illustrate amplitude and direction of differentspatial frequencies k_(m),m' * that are necessary to couple the inputm=0th mode to all output modes.

FIG. 7 represents regions of different refractive index in the body;

FIGS. 8(a), 8(b) 9(a), 9(b) 10(a) and 10(b) illustrate vectorsk_(m),m' * for star couplers having 2 and 4 output modes, respectively;

FIG. 11 is a block schematic diagram of an alternative apparatus formaking a diffraction means having a spatially varying refractive index;and

FIG. 12 is a simplified schematic diagram of a "shuffle net" lightwavecommunication system incorporating a limited-broadcast coupler and aplurality of user interfaces;

FIG. 13 is a connectivity graph for the shuffle net of FIG. 12; and

FIG. 14 is a block diagram of one of the user interfaces of FIG. 12.

DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

FIG. 1 shows an optical interconnector comprising a glass substrateformed by two plates 102 and 104, respectively. A diffraction means inthe form of body 106, of dielectric material, such as lithium niobate(LiNbO₃) formed as a Bragg volume hologram, is sandwiched between thetwo plates 102 and 104. For other suitable materials the reader isdirected to a paper entitled "Two-Wave Mixing in Nonlinear Media", IEEEJournal of Quantum Electronics, Vol. 25, No. 3, Mar. 19, 1989 which isincorporated herein by reference. Juxtaposed surfaces of the glassplates 102 and 104 are recessed to accommodate the block 106. Two arraysof single mode optical fibres 108 and 110, respectively, abut oppositefaces 112 and 114, respectively, of the block 106. The opposite faces112 and 114 are cylindrical sections and symmetrical. The distancebetween the faces 112 and 114, at their midpoints, is equal to theradius of curvature, d, of the surfaces 112 and 114.

The end portions 116 of the optical fibres 108, 110, where they abut theblock 106, are enlarged to about 100 microns diameter which is about tentimes the diameter of the typical single mode optical fibre. Thetransition between each single mode fibre and its enlarged end portionis gradual i.e. tapered.

The thickness of the dielectric body 106, is equal to the width of eachof the enlarged portions 116, i.e. about 100 microns for a 9×9 coupler,so that substantially all of the light incident upon its end faces 112,114 is channelled into the attached optical fibres. The optical fibres108 and 110 serve as sources or receivers, the sources being arranged totransmit "nearly plane wave" light beams.

The optical interconnector is represented schematically in FIG. 2. Thenumber of fibres in each array 108, 110 is N=2M+1. Thus there are N=2M+1nearly plane wave inputs directed from arcuate surface 112 towards thecentre of arcuate surface 114, and vice versa. The transit distance i.e.the distance between the arcuate surfaces 112 and 114 at theirmid-points is d and the arc length of each arcuate surface is D. Eachenlarged end portion 116 on the input array has a width a such that

    aN=D

The width a should be large enough compared to the spatial wavelength ofn(x,z), i.e., ##EQU7## The width of the body 106, i.e. the distance dbetween the arcuate surfaces 112, 114 at their midpoints, is defined as:##EQU8## The width should be large enough to satisfy the thick gratingcondition given later by Equation (3); while the geometry should alsomeet the condition defined later by Equation (28). The same argumentsapply to the output surface of the coupler. A simple investigation showsthat D increases as M² while d increases as M.

In use, a beam of light emanating from any one of the array of opticalfibres 108 will be diffracted by the thin film body 106 into a pluralityof modes, one for each of the array of optical fibres 110 at theopposite side of the body 106. Conversely, light emanating from any oneof the array of optical fibres 110 will be diffracted into a pluralityof modes, one for each of the array of optical fibres 108.

As shown in FIG. 2, the z ordinate extends in the direction of the axisjoining the middles of the arcuate faces 112, 114, and the x ordinate isperpendicular to it. The arcuate faces 112, 114 are actually cylindricalsegments. The refractive index of the block 106 is n(x,z). The number ofoptical fibres in each array, N, is 2M+1 and the angle between theoptical axes of adjacent optical fibres is θ₀ degrees.

The optical fibre whose optical axis coincides with the middle of thetwo arcuate surfaces 112 and 114, respectively, is deemed to be the Othmode and the modes on either side of that axis are numbers 1 to +M and 1to -M.

FIG. 3 illustrates refraction for a single perturbation term, the Othmode in the array of optical fibres 108. In FIG. 3(a), the angle ofrefraction is Mθ₀ degrees, resulting in the Mth mode being transmittedto the endmost optical fibre in the array 110. FIG. 3(b) shows that theOth mode is refracted at an angle (M-1(θ₀ degrees and FIG. 3(c) showsthat the Oth mode is refracted at an angle θ₀ degrees. The samerefractive index grating pattern will couple the O to Mth modes of thearray of optical fibres 110 to the Oth mode of the array of opticalfibres 108. The block 106 can thus be considered to be a plurality ofsub-holograms, each providing a different output mode for a given inputmode.

Each sub-hologram which, in effect, can be considered to be a 1×(2M+1),or (2M+1)×1 coupler, is formed by two-wave mixing on a holographic film.

FIG. 4(a) and FIG. 4(b) illustrate how the coupler embodying theinvention would couple the Mth mode and (M-2)th mode, respectively, toall output modes. For the Mth mode, the refractive index n(x,z) is givenas: ##EQU9## For the (M-2)th mode, the refractive index n(x,z) is givenas: ##EQU10##

FIG. 4(c) illustrates how all of the modes are provided to achieve N×N'coupling, the refractive index n(x,z) varying in accordance with theexpression: ##EQU11## Thus the block 106 comprises a holographic patterncharacterized by a spatial variation of this refractive index n(x,z).

Such a pattern can be implemented using known techniques, see forexample a Ph.D. by M. Tabiani entitled "Spatial Temporal Optical SignalProcessing", M.I.T., August 1979, a paper entitled "Bragg Gratings onInGaAsP/InP Waveguides as Polarization Independent Optical Filters", byC. Cremer et al, IEEE Journal of Lightwave Technology, vol. 7, No. 11,Nov. 1989, and also the disclosures of European patent application No.0,339,657, U.S. Pat. No. 4,705,344 and U.S. Pat. No. 4,838,630. All ofthese disclosures are incorporated herein by reference. The pattern maybe provided on a single film of photorefractive material (thick gratingor volume holography on a single crystal or film).

FIG. 5 illustrates manufacture of the body 106 with its spatiallyvarying refractive index for an N×N' coupler. The implementation isbased on two wave mixing employing a rotating mechanism, to mix E_(m)and E_(m) ' by varying m and m' in successive steps.

In each step, with m and m' fixed, the interaction of the two beamsE_(m) and E_(m) ' is written on the photorefractive media. Then keepingm fixed, we vary m' from M+1 th N-(M-1) and repeat the writing processof each combination of E_(m) and E_(m) ', respectfully. Next, we vary mfrom 1 to M and repeat the procedure.

FIG. 5 is a block schematic diagram of the apparatus for implementingsuch two-wave mixing, comprising two coherent light sources 502 and 504,respectively, mounted for rotation by two motors 506 and 508,respectively. The light sources 502 and 504 generate nearly plane wavesE_(m) and E'_(m), respectfully. The centre of rotation for both of themotors 506 and 508, is the middle of the arcuate surface 112 which isfurthest away as indicated at 510. The relative positions of the drivemotors 506 and 508 are controlled by drive control means 512 whichrotates the motors about point 510. The first motor, 506, rotates thefirst nearly plane wave source 502 (Em) such that its propagation vectork_(m) makes an angle ##EQU12## with the -z axis. Second motor 508 alignsthe second nearly plane wave source 504 (E_(m) ') such that itspropagation vector k_(m') makes an angle ##EQU13## with the -z axis. Fora fixed m, second motor 508 varies the k_(m') direction incrementallysuch that m+ varies between m'1 to N-(m-1). Then, by varying m, thefirst motor 506 will bring the first source 502 to the new position andthe process continues. In each position, the beams E_(m) and E_(m') fromthe two sources, 502 and 504 are mixed to form (print) a desired term ofEquation (8) on the photorefractive material. After printing all theterms of Equation (8), by body will have a refractive index varying inaccordance with the equation (8). When placed between the two circulararrays 108 and 110 of the coupler shown in FIG. 1, the body 106 willform an N×N' optical interconnection.

The coupling pattern can be modified by varying the intensities of thebeams E_(m) and E_(m) ' any particular step to provide other then N×N'coupling. The intensity is controlled by means of attenuation filters514 and 516 in the optical paths of light sources 502 and 504,respectively. The attenuation filters 514 and 516 are controlled bymeans of an intensity control means 518 which operates in conjunctionwith the drive means 512.

It is also possible to fabricate a star coupler which couplesselectively rather than broadcast. There are applications in which it isdesirable to couple, for example, one of a plurality of inputs to alimited number of a plurality of outputs. The photorefractive stratifiedBragg volume hologram for such a coupler could be made in a similarmanner to the full broadcast Bragg volume hologram describedhereinbefore with a refractive index varying according to the generalexpression: ##EQU14## where sin(γ_(m) d)=1 m=-M, . . . , 0, . . . , Mand where ##EQU15## with C being the speed of light, then the powercoupling coefficient between any input mode m and any output mode m'will be proportional to Δ_(m),m', an element of the routing matrix.##EQU16##

One application for such a selective coupler is high capacity local areanetworks. FIG. 12 illustrates a multihop perfect shuffle networkcomprising a passive optical star coupler 120 and a set of eight userinterfaces 121-128, respectively. Eight input ports 1-8 are distributedalong one curved face 129 of the coupler 120 and eight output ports1'-8' are distributed along opposed curved face 130. The interfaces121-128 comprise laser transmitters 131-138 and photodiode receivers141-148, respectively. The input ports 1-8 are connected to respectiveoutputs of laser transmitters 121-128 and output ports 1'-8' areconnected to respective ones of the inputs of photodiode receivers141-148.

The star coupler 120 comprises a stratified volume holographic mediumhaving a spatially-varying refractive index. As in the case of thecoupler of FIG. 1, the refractive index varies according to the generalexpression ##EQU17##

The transmitters 121-128 are each capable of transmitting signals witheither of two wavelengths, by selecting either of two lasers. Of course,a single laser which can be switched between two wavelengths might besubstituted. The receivers 141-148 each have a photodiode receiver stagefor detecting two wavelengths. These are not the same as the transmitterwavelengths but correspond to wavelengths of two other user interfacesto which the receiver is connected. When a signal from an individualtransmitter arrives at the corresponding input port, and is launchedinto the coupler 120, it will be directed to one or the other of twooutput ports depending upon its wavelength. For example, a signal withwavelength λ₁ transmitted from laser transmitter 121 to input port 1will be coupled to output port 5', whereas a signal at wavelength λ₂transmitted by way of the same input port 1 will be directed to outputport 6'.

In this particular case, the stratified volume hologram has a refractiveindex varying according to the expression ##EQU18## Hence, the coupler120 functions to couple 2 out of 8, i.e. each input port 1-8 can coupleto a predetermined two of the output ports 1'-8'.

The connectivity of the shuffle network of FIG. 12 is illustrated inFIG. 13. The network is a "perfect" shuffle network in that each usercan communicate with every other user, even though each individual userinterface has only two direct linkages to other user interfaces. Inorder to achieve this connectivity, some signals will be relayed. Forexample, if user 1 wishes to transmit a packet of data to user 6, userinterface 121 will append user 6's address onto the packet, selectwavelength λ₂, and launch the signal into input port 1. The signal willgo directly to output port 6' and thence to receiver interface 146 whereit will be demodulated, the address detected, and the packet deliveredto user 6.

If user 1 wishes to send a packet to user 8, user interface 121 willaddress the packet, select a wavelength λ₂ to direct the signal toreceiver interface 146 of user 6. In receiver interface 146, the addressinformation will be detected and indicate that the packet is to berelayed to receiver interface 144 of user 4 on λ12. In receiverinterface 144 the address will be detected and again indicate that thepacket is to be relayed. Consequently, user interface 124 selects awavelength of λ₈ and transmits the packet by way of input port 4 andoutput port 8' to receiver interface 148. In receiver interface 148, thesignal will be detected and the packet delivered to user 8.

FIG. 14 illustrates, as an example, receiver interface 141, whichcomprises a photodetector receiver stage 150 connected to output port1'. The photodetector receiver stage 150 includes two photodiodedetectors (not shown) for detecting signals having wavelengths λ₉ andλ₁₃, respectively. Detecting circuitry 151 decodes the addressinformation prefixed to the incoming signal. If the address is its own,it directs the incoming signal to a hardware interface 152 for user 1.If, on the other hand, the address indicates that the message is to berelayed, in which case it will also contain information as to which userinterfaces are in the relay chain. Laser transmitter stage 131 includesa selector 153 and lasers 154 and 155 having operating wavelengths λ₁and λ₂, respectively. Detecting means 151 will control selector 153 todirect the outgoing signal to the appropriate one of transmitters 154and 155.

When user 1 wishes to initiate a transmission, user hardware interface152 will prefix the message with the appropriate routing address anddetecting means 151 will select the appropriate one of lasers 154 and155 for its transmission. The limited or selective star coupler 120 canbe fabricated using similar techniques and apparatus as that illustratedin FIGS. 5 and 11 and described with respect to the manufacture of thefull broadcast star coupler.

By way of example, for a 9×9 limited-broadcast coupler, the input arraywidth is chosen such that ##EQU19## where MAX stands for maximum; and

    Mθ.sub.0 =0.4

Using M=4 for a 9×9 switch and a=100λ, D=900λ, where λ is the wavelengthof the optical signal and is equal to 2.5D, for λ≃1μm, the dimensionsare approximately 1mm×2.5mm in the x×z directions. In the y direction itis assumed to be larger.

It is preferable to expand the diameter of each single-mode input/outputfiber. This expansion can be done by using appropriate tapers. Beamexpansion ratios in the range of 5-10 are feasible with a correspondinginsertion loss per taper of less than 0.01-0.025 dB. By using thesenumerical values, the thick grating condition holds. The specifiedrouting matrix Δ can be constructed by the wave-mixing method asdiscussed earlier.

Although a skilled artisan should be able to implement the invention onthe basis of the foregoing description, th e following mathematicalexplanation is provided to facilitate an understanding of the conceptsupon which the invention is predicated.

Intuitive Analysis of Space-Varying Refractive Index Body

Referring again to FIG. 2, we define the m-th mode as a plane wavetravelling to the direction that makes an angle mθ₀ with the z axis;independent of y as:

    E=e.sup.j{ωt-k[x sin (mθ.sbsp.0.sup.)+z cos (mθ.sbsp.0.sup.)]}  C.C.                            (1)

where c.c. means complex conjugate of the first term, x, y and z arespatial coordinates, and ω and k refer to optical frequency and wavevector (propagation factor ##EQU20##

This analysis is based upon an intuitive Bragg diffraction approach asdisclosed by A. Yariv in the book "Optical Electronics", Holt, Rinehartand Winston, 1985, but modified to achieve appropriate mode interactionfor N×N' couplers.

In order to couple the m-th input mode to the m'-th output mode as shownin FIG. 2, we must establish the following pattern of refractive index:

    n(x,z)=1+Δ.sub.m,m' sin (K*.sub.m,m' ·I)    (2)

where Δ_(m),m' is the coupling coefficient between input m-th and outputm'-th modes and r represents dimensions of the space, where

    r=X·1.sub.x +Y·1.sub.y +Z·1.sub.z

and i is the unity vector.

The following constraints on the direction and amplitude of vectorspatial frequency K*_(m),m' must hold in order to satisfy theBragg-diffraction thick grating conditions according to A. Yariv and M.Tabiani, respectively, ##EQU21## where d is the thickness of the body106 and k refers to the optical wave vector. ##EQU22##

Coupling m=L-th Input Mode to N=2M+1 Output Modes

Based on the previous discussion on coupling the m=Lth input mode toN=2M+1 output modes (m'=-M, . . . ,0, . . . ,M), we must maintain thefollowing refractive index variation relation: ##EQU23## with Δ_(L),m'<1 plus conditions on K_(L),m' defined by Equations (3) to (6) with m=Land with m'=-M, . . . ,O, . . . ,+M.

As an example, consider vector K*_(L),m' for some specific cases likeM=2 and M=4 and plot K*_(L),m' for L=0.

FIG. 6A shows a plot of K*_(L),m' to couple L=0-th input mode to outputmodes m'=-2, -1, 0, 1 and 2. FIG. 6B shows a plot of K*_(L),m' to coupleL=0-th input mode to output modes m'=-4, -3, -2, -1, 0, 1, 2, 3, 4.

It should be realized that with the spatial varying refractive indexgiven by Equation (7) with the constraints introduced in Equations (3)to (6), only m=L-th input mode will interact with all other N=2M+1output modes (m'=-M, . . . ,0, . . . ,+M). The degree of interactiondepends on Δ_(L),m' which is a vector of Δ, the routing matrix. However,by the condition on n(x,z) defined in Equation (7), no other input mode(m≠L) can be strongly coupled to any of the N=2M+1 output modes. This isdue to the fact that none of the existing spatial vector frequenciesK*_(L),m' meet the conditions in Equations (4) to (6) for such an input.For more mathematical details, the reader is directed to the paper by M.Tabiani referred to hereinbefore.

Coupling N=2M+1 Input Spatial Modes to N=2M+1 Output Modes (m,m'=-M . .. ,O, . . . . ,+M)

In order to couple all the N=2M+1 input modes to all the N=2M+1 outputmodes, i.e. the case where N=N', the following refractive indexexpression needs to be maintained: ##EQU24## with Δm,m'<1 and K*_(m),m'satisfying the conditions defined by Equations (3) to (6) for allm,m'=-M, . . . ,0, . . . ,+M.

Mathematical analyses indicate that if

    Δ.sub.m,m' =Δ                                  (9)

and ##EQU25## where C is the speed of light, then the power couplingcoefficient among input/output modes will be the same and equal to 1/N,namely: ##EQU26## Such a power division is 100% efficient. Thissituation, with Δ_(m),m' constant, gives broadcast coupling, i.e. eachinput couples to every output.

If we take Δ_(m),m' from a specific preselected N×N' matrix Δ=. . .Δ_(m),m' . . . with, m,m'=-M, . . . ,M

then, the power of any arbitrary m-th input element will be distributedto all n=2M+1 output elements by a transmission coefficient proportionalto Δ² _(m),m' for all m'=-M, . . . ,O, . . . ,M.

In this case, the implementation is still based on two-wave mixing witha rotating mechanism and with an intensity control apparatus comprisingthe intensity control means 518 and attenuation filters 514, 516described earlier with reference to FIG. 5.

Each time we mix E_(m) and E_(m') with a fixed m and m', but with avariable intensity, the interaction of the two beams is written on thephotorefractive medium. Now, with a fixed m, we vary m' from m+1 toN-(m-1) while source intensities vary according to Δ² _(m),m'. Next, wevary m from 1 to M and we continue this procedure.

In the case of the selective or limited-broadcast coupler, Δ_(m),m' isan element of the Δ routing matrix and K_(m),m' must satisfy theconditions defined in equations 3 to 6 for all m,m'=-M, . . . ,O, . . .,O, . . . ,+M.

Mathematical analyses indicate that if ##EQU27## with C being the speedof light, then the power coupling coefficient between any input mode mand any output mode m' will be proportional to Δ_(m),m', an element ofthe routing matrix. Hence, because the coupling coefficient is notconstant, the coupler will attenuate some signals and not others,depending upon whether or not a particular propagation mode has beenselected.

Mathematical Analysis of Space-Varying Refractive Index Body

The following discussion is based on the mathematical analyses in thepaper by M. Tabiani supra. In this discussion we will see how inputm=L-th mode couples to output m'=(L+1), . . . , (L+M) modes with thespecific refractive index variation in space. This analysis will specifythe coupling coefficients among different input/output modes.

Mathematical Analysis of Space-Varying Refractive Index Slab

Consider the medium shown in FIG. 7 with the following refractive indexvariation in region II: ##EQU28## with |Δ_(L),m' |<1 and the conditionsgiven by Equations (3) to (6) for m=L. Notice that, for all mathematicalanalysis n(x,z) has been chosen to have M components, whereas forcoupling applications n(x,z) is assumed to have N=2M+1 components.Assume that the input wave is the sum of M+1 modes as: ##EQU29## whereD_(inc),m is the incidental wave coefficient of the m-th mode. Becauseof the form of the refractive index in Equation (12), the field inregion II will be as follows: ##EQU30## where D_(m) (z) is the m-thcoefficient of the wave in the second region.

defining E_(II) (x,z,t) by the summation term on the right in Equation(14), we can accommodate n(x,z) by using the wave equation: ##EQU31##

M. Tabiani had shown in the thesis referred to earlier, that twoequations (12) and (14) may be substituted into Equation (15) to obtainthe following coupled-mode equations: ##EQU32##

Equation (16) is the coupled-mode equation for the system shown in FIG.7 with n(x,z) given by Equation (12). We can see that input mode Lcouples simultaneously to output modes m=L+1, . . . , L+M, but inputmode (L+m') and output mode (L+m") with m'≠m" and m', m"≠0 not coupledwith each other, directly.

Thus Equation (16) shows that the refractive index n(x,z) given byEquation (12) serves the purpose, as stated earlier. A detailed analysisof the system governed by Equation (16) can be performed as we willdiscuss it in the following subsection.

Solution of the Mode-Equation

We shall see the solution of Equation (16) for the case of L=0 by meansof state-variable representation. Without loss of generality, we onlyneed to consider modes 0 through M. Thus, if we let D(z) be an (M+1)dimensional column vector with components D_(m) (z), we obtain:##EQU33## where A is an (M+1)×(M+1) matrix with elements ##EQU34##

Suppose the slab in region II (FIG. 7) is illuminated by an input waveof the type presented by Equation (13), then the field in region III is##EQU35## and φ(d) is the transition matrix associated with the stateEquation (17).

The transition matrix φ(z) can be found by a Fourier Transform methodsuch as is disclosed by R. W. Brackett in Chapter 11 of the bookentitled "Finite Dimensional Linear Systems", J. Wiley, New York, 1970.The result is as follows: ##EQU36##

Considering Equation (21) in the specific case of the full broadcast N×Ncoupler, where

    Δ.sub.0,i =Δ                                   (23)

    and

    sin (γ.sub.0 d)=1                                    (24)

we can reach the following conclusions. The 0-th input mode is dividedamong M output modes m'=1, . . . , M by the amplitude factor 1/√M orpower factor 1/M. The O-th input mode does not get coupled as depictedin FIG. 7, since cos(γ₀ d) is zero. However, referring to FIG. 2, sincethe distance between any input/output pair is not a constant, there willbe some power at these output modes.

If we take n(x,z) given by Equation (12) with any arbitrary L instead ofL=0; then L-th input mode couples simultaneously to M output modesm=L+1, . . . , L+M, but (L+M') and (L+M") with m'≠m" and m', m"≠0 notcoupled to each other, directly. Therefore, n(x,z) in Equation (8) willcouple all N=2M+1 input modes to all N=2M+1 output modes with a 100%efficiency.

We use the configuration in FIG. 2 such that N input elements areequally spaced on the surface of the outer circle, while each input isaligned with the centre of the circle. Based on this configuration, thedistance between the m-th input mode and m'-th output mode, d_(m),m' isno longer a constant, it depends on m, m' and θ₀ parameters, such thatfor small angles: ##EQU37## Therefore, we must choose the parameterssuch that ##EQU38## in order to keep Equation (24) valid for theconfiguration in FIG. 2. Then by properly choosing n(x,z) as given byEquation (8), for Δ_(m),m' =Δ and satisfying Equations (24) and (26),each input wave will be equally divided among the output array ports.

Considering Equation (21) in the alternative case of the selective orlimited broadcast coupler of FIG. 12, where Δ₀,i is chosen as thezero-th column of the routing matrix Δ and sin (γ_(m) d)=1 for m=0 wecan reach the following conclusions. The 0-th input mode is dividedamong the M output modes m'=1, . . . , M by the amplitude factor##EQU39## or the power factor ##EQU40##

As in the broadcast case, the 0-th mode does not go through since cos(γ₀d) tends to zero. If we take n(x,z) from equation 12 with any arbitrarynon-zero L; the L-th input mode couples simultaneously to M output portsand no other input mode couples to any output mode. However, n(x,z) inequation 8 will couple all the N=2M+1 input modes to all the 2M+1 outputmodes with a coupling coefficient proportional to Δ_(m),m', the elementsof the routing matrix Δ.

As before, the N input elements are equally spaced on the surface of theouter circle, while each input is aligned with the centre of the circle.Also, the distance between the m-th input mode and the m'-th outputmode, d_(m),m', again depends on m,m' and θ₀ parameters, such that forsmall angles: ##EQU41## In this case, however, the parameters are chosensuch that: ##EQU42## in order to keep equation 25 valid for any m-thinput mode for the configuration. Proper choice of n(x,z) as given byequation 8, for Δ_(m),m', selected by the coupler routing matrix andsatisfying equation 24 for any m and satisfying equation 27a, willresult in each input wave being divided among other ports with acoupling coefficient proportional to Δ_(m),m'.

Pattern for K*_(m),m'

To realize the refractive index given by Equation (8), let us considerK*_(m),m', as a vector whose amplitude and direction satisfy theconditions given by Equations (4) to (6) for m,m'=-M, . . . , 0,1,2,3, .. . , M.

For small angles as

    |Mθ.sub.0 |<<π,                 (28)

by carefully examining the K*_(m),m' vectors, we discover an interestingpattern which can easily be realized by wave mixing.

For simplicity, let us consider K*_(m),m' pattern in the following twosimple cases:

a) M=2 for a 5×5 star coupler

b) M=4 for a 9×9 star coupler

FIG. 8A is a plot of K*_(m),m' for M=2, for a 5×5 star coupler (m,m'=-2,-1, 0, 1, 2). FIG. 8B is a plot of K*_(m),m' for M=4, 9×9 star coupler(m,m'=-4, -3, -2, -1, 0, 1, 2, 3, 4). If we examine these vectorscarefully as depicted in FIGS. 9A and 9B, tips of the K*_(m),m' vectorsare located on different circles all with the same radius.

A more careful examination of these vectors as shown in FIGS. 10A and10B, indicates the radius;

    R=|k|                                    (29)

where K represents the optical wave vector.

For an arbitrary M, there are M circles on each side, each with a radiusR=|k|. If we number these circles as shown in FIGS. 9A and 9B, on thefirst circle there are 2M vector tips. On the second circle, there are2(M-1) vector tips and so on. That is, on the i-th circle there are2(M-i+1) vector tips.

Wave Mixing Realization

Interaction of two laser beams inside a photorefractive medium, when,the two beams have the same frequency, forms a stationary interferencepattern. Its intensity makes a spatial variation inside the medium andproportionally creates refractive index variations in space as describedby Pochiz Yeh in his paper entitled "Two-Wave Mixing in Non-LinearMedia", IEEE Journal of Quantum electronics, vol. 25, No. 3, Mar. 19,1989, which is incorporated herein by reference.

The electric field of these waves can be expressed as

    E.sub.i =Ae.sup.j(ωt-k.sbsp.i.sup..f) +C.C. i=1, . . . , 2M+1 (30)

where

    |k.sub.i |=|k|         (31)

with the direction of k_(i) being a variable.

According to Pochiz Yeh, the refractive index perturbation will be aperiodic function in space with a spatial frequency k_(m) -k_(m') whenE_(m) and E'_(m) are mixed.

Consider two previously described examples on construction of K*_(m),m'in creating the necessary refractive index given by Equation (8) for a5×5 and a 9×9 coupler (see FIG. 10).

a) M=2, for a 5×5 star coupler:

In this case, we need to have N=5 waves E₁, E₂, E₃, E₄ and E₅ as shownin FIG. 10A to create all corresponding K*_(m),m'. In order to configurefour vectors located on the first circle, we must mix E₁ with E₂, E₃, E₄and E₅, To construct two vectors K*_(m),m' on the second circle (and thelast for M=2 case) according to the specific geometry shown in FIG. 10A,we need to mix E₂ with E₃, E₄.

b) M=4, for a 9×9 star coupler:

As shown in FIG. 10B we need to have N=9 waves (E₁ . . . E₉) to createall corresponding K*_(m),m'. In order to configure eight vectorsK*_(m),m' located on the first circle, we must mix E₁ with E₂ to E₉. Toconstruct six vectors K*_(m),m' located on the second circle, we mustmix E₂ with E₃ to E₈. For four vectors K*_(m),m' located on the thirdcircle, we must mix E₃ with E₄ to E₇. Finally, in order to create twovectors K*_(m),m' located on the fourth circle (the last for thisexample) we must mix E₄ with E₅ and E₆.

Based on these examples, with no loss in generality, to create allvectors K*_(m),m' in FIGS. 10A and 10B for an N×N' coupler with N=2M+1,we have to mix ##EQU43##

Notice that, all of these waves have the same frequency but differentdirections. E₁ has an angle -Mθ₀ /2 with -z direction and E_(i) has anangle θ₀ with E_(i-1), and so on. Therefore, we have to have only twowaves at the same frequency. We mix the first one in the proposed E₁direction. Then by rotation, we bring the second one in the direction ofE₂, E₃, . . . and E_(N), respectively. In each position, we mix thefield with the first one. In the next round, we bring the first one inthe proposed E₂ direction and rotate the second field to bring it intothe direction of E₃, . . . and E_(N-1). In each position we mix thefield with the first one. The procedure is continued. In the last step,the first field is placed in the E_(M) direction and the second wave onthe E_(M+1) and the E_(M+2) direction while mixing the pairs in eachposition. Therefore, with this method, by two wave mixing we can createall vectors K*_(m),m' corresponding to n(x,z) given by Equation (8).

DESIGN REQUIREMENT AND AN EXAMPLE

The proposed N×N star optical coupler is shown in FIG. (2). There areN=2M+1 nearly plane wave inputs directed towards the center of thecircular input surface with a diameter D. Each element of the inputarray has a width a such that

    aN=D                                                       (32)

The width a should be large enough compared to the spatial wavelength ofn(x,z), i.e., ##EQU44## The width of the slab is d and is defined as:##EQU45## The slab width should be large enough to satisfy the thickgrating condition given by Equation (3); while the geometry should alsomeet the condition defined by Equation (28). The same arguments apply tothe output surface of the coupler. A simple investigation shows that Dincreases as M² while d increases as M. The medium with space-varyingrefractive index n(x,z) given by Equation (8) may be created by the twowave mixing methods mentioned herein for a given N.

In order to obtain 100% efficiency, the parameters are selected in a waythat conditions given by Equations (4), (6), (10) and (27b) aresatisfied.

For the selective or limited-broadcast coupler, Δ_(m),m' is determinedby the routing matrix

    Δ=(Δ.sub.m,m')

To achieve wavelength division multiplexing, let us assume that λ canvary between λ-δ to λ+δ. The coupler will still operate if we keep theperturbation on term ##EQU46## of Equation (10) to be much smaller thanπ. This can be done by limiting δ such that: ##EQU47## which means thatthe optical signal bandwidth is limited by the geometry of the coupler.

EXAMPLE

For a 9×9 coupler a is chosen such that Equation (33) is satisfied as##EQU48## where MAX stands for maximum. Also, the condition given byEquation (26) is satisfied by choosing

    Mθ.sub.0 =0.4                                        (36)

Using M=4 for a 9×9 star coupler given by Equation (4) we will have:

    a=100λ                                              (37)

and

    D=900λ                                              (38),

where λ is the wavelength of the optical signal and d is equal to 2.5D.That is, for λ≃1 μm the dimensions are approximately 1 mm×2.5 mm in thex by z direction. In the y direction it is assumed to be larger.

Equation (37) points to expanding the diameter for each single-modeinput/output fibre. This expansion can be done by using appropriatetapers. Beam expansion ratios in the range of 5-10 are feasible with acorresponding insertion loss per taper of less than 0.01-0.025 dB. Byusing these numerical values, the thick grating condition governed byEquation (3) holds. The refractive index n(x,z) in Equation (8) for agiven M will be created as described hereinbefore with two wave mixingand rotation operation. Parameter Δ_(m),m' should be chosen such thatthe conditions in Equation (9), (10) and (26) are satisfied.

It should be appreciated that, since N was defined as 2M+1, the numberof ports is an odd number. In the practical embodiments, where an evennumber of ports is preferred, the ninth port is simply not used. Inessence, a row of zeros will appear in the connectivity matrix.

Bandwith Considerations

To achieve wavelength division multiplexing, we need to know thebandwidth of the limited-broadcast coupler. Let us assume that theoptical signals with wavelengths λ_(i) varying between λ-δ and λ+δ cango through the coupler without any major attenuation. We would like tocalculate the 3-dB bandwidth for the coupler. The coupler will respondto signals, if we keep the wavelength perturbation on ##EQU49## ofequation 11a to be much smaller than π. To calculate the 3-dB bandwidth,instead of equation 11a, we must have: ##EQU50## Since ##EQU51## the3-dB bandwidth will be a function of d, M and the routing matrixelements. However, the coefficients must satisfy the condition expressedby equation 27b, as well. To calculate the bandwidth in general, we willalso use the condition expressed by equations 32, 34 and 36. Then wewill present some numerical data for the special case of the 9×9coupler.

Applying conditions expressed by equations 32, 34, and 36 in equation27b, we will arrive at the following equation; ##EQU52## where I₀ is aninteger. With ##EQU53## approximately, we will have: ##EQU54##

Using the above result in equation 39 will result in the followingconstraint on the available bandwidth in wavelength domain: ##EQU55##where in equation 42, λ is the light wavelength, N is the number ofinput.output ports, and I₀ is an integer.

To maximize the available bandwidth, we choose I₀ =1, i.e. ##EQU56##

The bandwidth presented in equation 43 is the available band around thenominal central wavelength λ.

As apparent from the periodic nature of equation 11a, such a bandwidthas expressed by equation 43 is also available around all otherwavelengths spaced by an integer multiple of Δλ form λ where: ##EQU57##

That is, any other wavelength that produces a phase shift proportionalto an integer multiple of 2π inside the argument of the sine function inequation 11a has available around it an equivalent amount of 3-dBbandwidth.

For the special case of a 9×9 coupler, where N=9 and for N=16, theavailable maximum bandwidth is about 3 nm and 1 nm, respectively. Ingeneral, by using the number of input/output ports N, we can useequation 43 to find the maximum available band.

Such a coupler can be designed around the central wavelength λ₀ fordense wavelength division multiplexing applications. All wavelengthsused around λ₀ that fall within the 3-dB band of the coupler will getthrough the coupler. Going back to FIG. 12, we can choose 16 wavelengthsaround λ₀ such that they fall within the 3-dB band of the coupler. Byforming the proper holographic patterns on the photosensitive slab, theperfect shuffle connectivity can be established.

To increase the coupling capacity, one way is to cascade severalcouplers with mutually overlapping passbands and use wavelengths withinthe overlapped regions of the band as a means of connecting couplers.Hence, we can build economy-of-scale into the coupler design. Anotheralternative is to select the wavelengths used in the WDM network suchthat their values match those at the peaks of the sine function inequation 11a. Using the latter method, the coupling efficiency remainsat its peak.

FIG. 11 illustrates an alternative apparatus for preparing a diffractionmeans with a spatially varying refractive index as describedhereinbefore. The block of photorefractive material 106' is positionedin a recess 1102 in a jig 1104. The jig 1104 has a plurality of opticalfibres in two arrays 1108 and 1110, respectively. These arrays ofoptical fibres correspond to the arrays of optical fibres 108 and 110,respectively, in the optical interconnector shown in FIG. 1. Each of theoptical fibres in array 108 is connected to a respective one of aplurality of light sources 1112. The light sources may be any commercialsingle mode source. Likewise, each of the optical fibres in array 110 isconnected to a respective one of an array of light sources 1114. Lightsources 1112 are connected to drive means 1116 and light sources 1114are connected to drive means 1118. The drive means are controlled bycontrol means 1120 which selectively and sequentially energizes thelight sources in pairs to irradiate the block 106' in order to "write"the spatially varying refractive index described with respect to FIG. 1.

As mentioned previously, with reference to the embodiment of FIG. 5,selective coupling, i.e. N is not the same as N', may be achieved simplyby varying the intensity of the light sources so as to omit to write thephotorefractive material at any position where no coupling is required.The embodiment of FIG. 11, can be modified to achieve this quite easilyby controlling the individual light sources by way of their respectivedrive means 1116 and 1118. Thus intensity control means 1122 operates inconjunction with drive indexing means to vary the intensity at theappropriate positions.

The embodiments of the invention described herein are by way of example.Various modifications and alternatives may be apparent to one skilled inthe art without departing from the scope of the invention which isdefined by the claims appended hereto.

The coupler described as a specified embodiment has an odd number ofinputs and outputs if could be modified quite readily to provide an evennumber of inputs and outputs, for example by omitting the 0-th mode.Moreover, although in the described embodiment the number of inputs isthe same as the number of outputs, they could be different if sodesired. This could be achieved quite readily by omitting to "write" thespecific part of the diffraction pattern as described with reference toFIGS. 5 and 11.

We claim:
 1. An optical interconnection device comprising a volume Braggdiffraction means, a first plurality (m) of optical elements spacedapart in a plane and a second plurality (m') of optical elements spacedapart in the same plane, said volume Bragg diffraction means extendingin said plane between said first plurality of elements and said secondplurality of elements, the first plurality of elements corresponding todiffraction orders of light beams from individual ones of said secondplurality of elements and the second plurality of elements correspondingto diffraction orders of light beams from individual ones of said firstplurality of elements, said diffraction means having its refractiveindex varying spatially according to the expression: ##EQU58## where xand z are coordinates of said plane;K*_(m),m' is the spatial frequencyvector; m and m' take on integer values equal to the first plurality andsecond plurality, respectively; Δ_(m),m' is the coefficient of couplingbetween m and m'; and r is the spaced vector,the spatial frequencyvector K*_(m),m' being determined according to the expression ##EQU59##k is the optical wave vector and ##EQU60## where θ ₀ is the anglebetween adjacent diffraction orders; and ##EQU61## where d is thethickness of the volume diffraction means in a direction transverse tosaid plane.
 2. An optical interconnection device as claimed in claim 1,comprising a body having cylindrical convex opposed faces, respectivecylindrical axes of faces being mutually parallel, said volume Braggdiffraction means being provided in said body such that its refractiveindex varies spatially and periodically in a plane substantiallyperpendicular to said cylindrical axes, such that a parallel light beamincident upon one of said faces of the body in said plane at apredetermined angle and with the electric field vector of such lightbeam extending substantially parallel to said cylindrical axes will bediffracted to provide said diffraction modes at the other of saidopposed faces.
 3. A device as claimed in claim 2, wherein thediffraction means is arranged to couple substantially all of the lightfrom a said light beam to the corresponding diffraction orders.
 4. Adevice as claimed in claim 2, wherein said optical elements compriseoptical waveguides, each of said optical waveguides having an opticalaxis aligned with a corresponding one of said diffraction orders, suchthat the respective optical axes of each array converge at a position onthe other of said arrays.
 5. A device as claimed in claim 4, whereinsaid position is at the middle of said other of said arrays.
 6. A deviceas claimed in claim 4, wherein each said optical waveguide is coupled toa source or receiver.
 7. A device as claimed in claim 2, wherein thethickness of said body in the direction of the cylinder axes of saidopposed faces is at least equal to the width of the light beams.
 8. Adevice as claimed in claim 1 or 2, wherein the refractive index variessuch that the said first plurality and said second plurality differ innumber.
 9. A device as claimed in claim 1, wherein said optical elementscomprise sources and/or receivers, each of said optical elements havingan optical axis aligned with a corresponding one of said diffractionorders.
 10. A device as claimed in claim 1 wherein the diffractionorders comprise an equal number of orders either side of a zero orderand said refractive index of the body varies spatially in accordancewith the expression: ##EQU62## where x and z are coordinates of saidplane; d is the radius of curvature of the curved faces;K*_(m),m' is thespatial frequency vector; m is an input position or mode, correspondingto one optical axis; r is the space vector; and the total number ofelements or modes (N), =2M+1.
 11. A device as claimed in claim 1,wherein said optical elements comprise optical waveguides.
 12. Anoptical interconnection device comprising diffraction means in the formof a body having cylindrical opposed faces and a refractive index whichvaries spatially and periodically in one plane of the body, such that aplanar light beam incident upon one of said faces of the body in saidplane at a predetermined angle and with the electric field of such lightbeam extending in the same direction as the cylindrical axes of saidcylindrical opposed faces, will be refracted to emerge at a plurality ofdiscrete angles determined by the spatially varying refractive index,such incident light being distributed substantially equally among theplurality of output refracted beams.
 13. Apparatus for making a volumediffraction means for an optical interconnection device for couplinglight beams between a first plurality (m) of optical elements spacedapart in a plane and a second plurality (m') spaced apart in said plane,by exposing a body of photorefractive material to radiation from aplurality of mutually coherent light sources to record resultinginterference patterns such that the refractive index of the body, afterexposure, will vary spatially according to the expression: ##EQU63##where x and z are coordinates of said plane; K*_(m),m' is the spatialfrequency vector;m and m' take on integer values equal to the firstplurality and second plurality, respectively; Δ_(m),m' is thecoefficient of coupling between m and m'; and r is the space vector, thespatial frequency vector K*_(m),m' being determined according to theexpression ##EQU64## k is the optical wave vector and ##EQU65## whereθ_(v) is the angle between adjacent diffraction orders; and ##EQU66##where d is the thickness of the volume diffraction means in a directiontransverse to the common plane, the apparatus comprising at least onepair of optical elements for emitting said radiation and means forcontrolling said optical elements to emit radiation simultaneously andfor a predetermined length of time from different pairs of predeterminedpositions, the positions of each pair being spaced apart in a commonplane through said body, one said position corresponding to adiffraction order for a light beam from the other position of said pair.14. Apparatus as claimed in claim 13, further comprising intensitycontrol means for varying the intensity of said light at predeterminedpositions to vary said coefficient of coupling Δ_(m),m'.
 15. Apparatusas claimed in claim 13, wherein a single said pair of optical elementsare movable between said different pairs of predetermined positions. 16.Apparatus as claimed in claim 13, wherein said optical elements arearranged in arrays, each optical element disposed at a positioncorresponding to a said diffraction order, and said means forcontrolling is operable to effect radiation from a first pair of sourcesa first pair of predetermined positions to record a first interferencepattern, and a second pair of said sources at a second pair ofpredetermined positions to record a second interference pattern. 17.Apparatus as claimed in claim 16, further comprising a support for asaid body of photorefractive materialsaid optical elements being in twocoplanar arrays, one array each side of the support and with theircommon plane extending through said support, the elements in each arraybeing positioned so as to emit coherent light beams, each having aplanar wavefront, in respective directions extending radially of aprescribed position of an element in the other of said arrays andmutually spaced according to said diffraction orders.
 18. A method ofmaking a volume Bragg diffraction means for an optical interconnectiondevice for coupling a first plurality of optical elements spaced apartin a plane and a second plurality of optical elements spaced apart insaid plane, the first plurality of optical elements corresponding todiffraction orders of light beams from individual ones of the secondplurality of optical elements and the second plurality of opticalelements corresponding to diffraction orders of light beams fromindividual ones of the first plurality of optical elements, such thatthe refractive index of the body, after exposure, will vary spatialaccording to the expression: ##EQU67## where x and z are coordinates ofsaid plane;K*_(m),m' is the spatial frequency vector; m and m' take oninteger values equal to the first plurality and second plurality,respectively; Δ_(m),m' is the coefficient of coupling between m and m';and r is the space vector,the spatial frequency vector K*_(m),m' beingdetermined according to the expression ##EQU68## k is the optical wavevector and ##EQU69## where θ₀ is the angle between adjacent diffractionorders; and ##EQU70## where d is the thickness of the volume diffractionmeans, said method comprising the steps of: (i) exposing a body ofphotorefractive material for a predetermined length of time to radiationfrom a pair of coherent light sources of the same wavelength, one sourcedisposed at a first predetermined position corresponding to an elementof said first plurality and the other disposed at a positioncorresponding to a diffraction order thereof, to record a firstinterference pattern; and (ii) exposing the body for a secondpredetermined length of time to radiation from said one source at saidfirst predetermined position and a second source at a positioncorresponding to a different one of the second plurality of diffractionorders; (iii) repeating step (ii) for each different one of the secondplurality of diffraction orders; (iv) repeating steps (i), (ii) and(iii) with said one source at positions corresponding to each of thefirst plurality of elements.
 19. A method as claimed in claim 18, saidpair of mutually coherent light sources in the first exposure step (i)and second exposure step (ii) are the same, at least one of said pair ofsources being repositioned between steps (i) and (ii).
 20. A method asdefined in claim 18, wherein said radiation is provided by means of afirst planar array of elements disposed at positions corresponding tothe first array of optical elements and a second planar array ofelements disposed at positions corresponding to the second plurality ofoptical elements, the arrays being coplanar and the body intersectingtheir common plane, said pair of sources comprising a source from eacharray, different pairs of said sources being selected sequentially foreach exposure step.
 21. A method as claimed in claim 20, wherein theintensity of the light from said sources is varied at predeterminedpositions so as to vary said refractive index to couple an incidentlight beam to selected ones of said diffraction orders, and where θ₀ isthe angle between optical axes of adjacent inputs.